What is expand (-1/3 x+1)^3 ?

The solution to expand (-1/3 x+1)^3 is (-x^3+9x^2-27x+27)/(27)

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expand (-1/3 x+1)^3

expand

(- \frac{1}{3} x + 1)^{3}

\frac{- x ^{3} + 9 x ^{2} - 27 x + 27}{27}

Solution steps

(- \frac{1}{3} x + 1)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(- \frac{1}{3} x + 1)^{3} = (- \frac{1}{3} x)^{3} + 3 (- \frac{1}{3} x)^{2} \cdot 1 + 3 (- \frac{1}{3} x) \cdot 1^{2} + 1^{3}

= (- \frac{1}{3} x)^{3} + 3 (- \frac{1}{3} x)^{2} \cdot 1 + 3 (- \frac{1}{3} x) \cdot 1^{2} + 1^{3}

Simplify

(- \frac{1}{3} x)^{3} + 3 (- \frac{1}{3} x)^{2} \cdot 1 + 3 (- \frac{1}{3} x) \cdot 1^{2} + 1^{3} : \frac{- x ^{3} + 9 x ^{2} - 27 x + 27}{27}

= \frac{- x ^{3} + 9 x ^{2} - 27 x + 27}{27}

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(4 sin (3 x) csc (2 x) - 3 tan (x)) csc (x) - 4

What is expand (-1/3 x+1)^3 ?
The solution to expand (-1/3 x+1)^3 is (-x^3+9x^2-27x+27)/(27)